Precalculus Examples

(- 6, 0)

$(- 6, 0)$ ,

(0, 6)

$(0, 6)$

Step 1

Slope is equal to the change in

y

$y$ over the change in

x

$x$ , or rise over run.

m = \frac{change in y}{change in x}

$m = \frac{change in y}{change in x}$

Step 2

The change in

x

$x$ is equal to the difference in x-coordinates (also called run), and the change in

y

$y$ is equal to the difference in y-coordinates (also called rise).

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Step 3

Substitute in the values of

x

$x$ and

y

$y$ into the equation to find the slope.

m = \frac{6 - (0)}{0 - (- 6)}

$m = \frac{6 - (0)}{0 - (- 6)}$

Step 4

Simplify.

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Step 4.1

Reduce the expression by cancelling the common factors.

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Step 4.1.1

Cancel the common factor of

6 - (0)

$6 - (0)$ and

0 - (- 6)

$0 - (- 6)$ .

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Step 4.1.1.1

Rewrite

6

$6$ as

- 1 (- 6)

$- 1 (- 6)$ .

m = \frac{- 1 \cdot - 6 - (0)}{0 - (- 6)}

$m = \frac{- 1 \cdot - 6 - (0)}{0 - (- 6)}$

Step 4.1.1.2

Factor

- 1

$- 1$ out of

- 1 (- 6) - (0)

$- 1 (- 6) - (0)$ .

m = \frac{- 1 (- 6 + 0)}{0 - (- 6)}

$m = \frac{- 1 (- 6 + 0)}{0 - (- 6)}$

Step 4.1.1.3

Reorder terms.

m = \frac{- 1 (- 6 + 0)}{0 - 6 \cdot - 1}

$m = \frac{- 1 (- 6 + 0)}{0 - 6 \cdot - 1}$

Step 4.1.1.4

Factor

6

$6$ out of

- 1 (- 6 + 0)

$- 1 (- 6 + 0)$ .

m = \frac{6 (- 1 (- 1 + 0))}{0 - 6 \cdot - 1}

$m = \frac{6 (- 1 (- 1 + 0))}{0 - 6 \cdot - 1}$

Step 4.1.1.5

Cancel the common factors.

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Step 4.1.1.5.1

Factor

6

$6$ out of

0

$0$ .

m = \frac{6 (- 1 (- 1 + 0))}{6 (0) - 6 \cdot - 1}

$m = \frac{6 (- 1 (- 1 + 0))}{6 (0) - 6 \cdot - 1}$

Step 4.1.1.5.2

Factor

6

$6$ out of

- 6 \cdot - 1

$- 6 \cdot - 1$ .

m = \frac{6 (- 1 (- 1 + 0))}{6 (0) + 6 (1)}

$m = \frac{6 (- 1 (- 1 + 0))}{6 (0) + 6 (1)}$

Step 4.1.1.5.3

Factor

6

$6$ out of

6 (0) + 6 (- - 1)

$6 (0) + 6 (- - 1)$ .

m = \frac{6 (- 1 (- 1 + 0))}{6 (0 + 1)}

$m = \frac{6 (- 1 (- 1 + 0))}{6 (0 + 1)}$

Step 4.1.1.5.4

Cancel the common factor.

$m = \frac{6 (- 1 (- 1 + 0))}{6 (0 + 1)}$

Step 4.1.1.5.5

Rewrite the expression.

$m = \frac{- 1 (- 1 + 0)}{0 + 1}$

Step 4.1.2

Add

$- 1$ and

$0$ .

$m = \frac{- 1 \cdot - 1}{0 + 1}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply

$- 1$ by

$- 1$ .

$m = \frac{- 1 \cdot - 1}{0 + 1}$

Step 4.2.2

Add

$0$ and

$1$ .

$m = \frac{- 1 \cdot - 1}{1}$

Step 4.3

Simplify the expression.

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Step 4.3.1

Multiply

$- 1$ by

$- 1$ .

$m = \frac{1}{1}$

Step 4.3.2

Divide

$1$ by

$1$ .

$m = 1$

Step 5